### Abstract

The Choquet and the Sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required. However, their applicability is restricted because of the special operations used in the construction of these integrals. Therefore, we provide a concept of integrals generalizing both the Choquet and the Sugeno case. For functions with values in the nonnegative real numbers, universal integrals are introduced and investigated, which can be defined on arbitrary measurable spaces and for arbitrary monotone measures. For a fixed pseudomultiplication on the nonnegative real numbers, the smallest and the greatest universal integrals are given. Finally, another construction method for obtaining universal integrals is introduced, and the restriction to the unit interval, i.e., to fuzzy integrals, is considered.

Original language | English |
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Article number | 5361437 |

Pages (from-to) | 178-187 |

Number of pages | 10 |

Journal | IEEE Transactions on Fuzzy Systems |

Volume | 18 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 1 2010 |

### Keywords

- Aggregation
- Choquet integral
- Pseudomultiplication
- Sugeno integral
- Universal integral

### ASJC Scopus subject areas

- Control and Systems Engineering
- Computational Theory and Mathematics
- Artificial Intelligence
- Applied Mathematics

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## Cite this

*IEEE Transactions on Fuzzy Systems*,

*18*(1), 178-187. [5361437]. https://doi.org/10.1109/TFUZZ.2009.2039367